Jeg tror, at sandheden kommer frem, hvis man tør være ærlig.

Yes. At introduces a subordinate clause after Jeg tror and works like English that in I think that ....

So:

• Jeg tror = I think
• at sandheden kommer frem = that the truth comes out / is revealed

Just like in English, that can often be left out. Danish can also sometimes omit at, especially in less formal style:

• Jeg tror, at sandheden kommer frem ...
• Jeg tror sandheden kommer frem ...

Both are possible, but at is very common and perfectly natural.

They mark subordinate clauses.

In this sentence, there are two subordinate clauses:

• at sandheden kommer frem
• hvis man tør være ærlig

Many Danish writers use commas to show where those clauses begin. However, in modern Danish, the start comma is optional, so you may also see:

Jeg tror at sandheden kommer frem hvis man tør være ærlig.

So the commas are not about a pause in speech as much as about clause structure.

Because sandheden means the truth, while sandhed means truth in a more general or indefinite sense.

Danish usually puts the definite article at the end of the noun:

• en sandhed = a truth
• sandheden = the truth

Here the sentence is talking about the truth as a specific idea, so sandheden is the natural form.

Komme frem is a very common verb expression. Literally it can mean come forward or come out, but in this kind of sentence it means something like:

• come out
• be revealed
• become clear

So sandheden kommer frem is an idiomatic way to say that the truth is eventually revealed.

This is worth learning as a whole expression. Komme by itself just means come, but komme frem has a more specific meaning.

No, not in this sentence.

Hvis is used for a condition, so it means if:

• hvis man tør være ærlig = if one dares to be honest

Om is usually used for whether, not conditional if:

• Jeg ved ikke, om han kommer. = I don’t know whether he is coming.

So here hvis is the correct choice because the sentence gives a condition.

Here man is the Danish indefinite pronoun, meaning:

• one
• you in a general sense
• people

So hvis man tør være ærlig means something like if you dare to be honest or if one dares to be honest.

It does not mean an adult male person here.

This use of man is extremely common in Danish when speaking generally.

Because turde often behaves like a modal verb in Danish, so it is followed by a bare infinitive.

That means you say:

• man tør være ærlig

not:

• man tør at være ærlig

This is similar to English dare be honest more than dare to be honest, although English usually prefers to there. In Danish, after tør, the infinitive normally comes without at.

Tør is the present-tense form of the verb turde, which means to dare.

So:

• infinitive: turde
• present: tør

That makes:

• man tør = one dares / you dare

It is an irregular verb, so it is worth memorizing rather than trying to build it from a regular pattern.

Because ærlig is the basic adjective form, and here it is used after være to describe man.

• at være ærlig = to be honest

You use ærligt in other situations, for example with a neuter noun or as an adverb:

• Det er ærligt ment.
• Han taler ærligt.

But with man as a person-like subject, ærlig is the normal form.

These are subordinate clauses, so the word order is the normal subject + verb order:

• sandheden kommer frem
• man tør være ærlig

That is different from main-clause Danish, where the finite verb is typically in second position.

A very useful thing to notice is what happens if you add a word like ikke:

• Jeg tror, at sandheden ikke kommer frem ...

In a subordinate clause, sentence adverbs like ikke usually come before the finite verb. That is one of the clearest signs that you are in a subordinate clause.

Because Danish often uses a verb plus a separate adverb or particle as a fixed expression.

So here:

• komme frem is written as two words
• in finite forms, it stays split: kommer frem
• in the infinitive, it is still two words: at komme frem

This is similar to English combinations like come out or show up, which are also written as separate words.

So it is best to learn komme frem as a unit, even though it is spelled as two words.

Because it expresses a general belief or general truth, not just one specific event happening right now.

• Jeg tror = I think
• sandheden kommer frem = the truth comes out
• hvis man tør være ærlig = if one dares to be honest

Danish often uses the present tense for general statements, just like English does:

• Honesty helps
• The truth comes out

So the present tense is the natural choice here.